Can Fregeans have 'I'-thoughts?

We examine how Frege?s contrast between identity judgments of the forms ?a=a? vs. ?a=b? would fare in the special case where ?a? and ?b? are complex mental representations, and ?a? stands for an introspected ?I?-thought. We first argue that the Fregean treatment of I-thoughts entails that they are what we call ?one-shot thoughts?: they can only be thought once. This has the surprising consequence that no instance of the ?a=a? form of judgment in this specific case comes out true, let alone a priori true. This further reinforces Glezakos?s objections against the set-up of Frege?s puzzle, while also raising what we think is an acute problem for Fregeans, insofar as I-thought (and indexical thinking more generally), understood in their way, turns out to be incompatible with some basic features of rationality.